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Central Limit Theorem for Markov Chains

  • Anirban DasGupta
Part of the Springer Texts in Statistics book series (STS)

Keywords

Markov Chain Invariant Measure Central Limit Theorem Simple Random Walk Stationary Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bremaud, P. (1999). Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queue, Springer, New York.Google Scholar
  2. Diaconis, P. and Stroock, D. (1991). Geometric bounds for eigenvalues of Markov chains, Ann. Appl. Prob., 1(1), 36–61.MATHCrossRefMathSciNetGoogle Scholar
  3. Dobrushin, R. (1956a). Central limit theorems for non-stationary Markov chains, I, Teor. Veroyatnost Primerien, 1, 72–89.MathSciNetGoogle Scholar
  4. Dobrushin, R. (1956b). Central limit theorems for non-stationary Markov chains, II, Teor. Veroyatnost Primerien, 1, 365–425.Google Scholar
  5. Doeblin, W. (1938). Sur deus problemes de M. Kolmogoroff concernant les chaines denombrables, Bull. Soc. Math. France, 52, 210–220.MathSciNetGoogle Scholar
  6. Doob, J.L. (1953). Stochastic Processes, John Wiley, New York.MATHGoogle Scholar
  7. Fill, J. (1991). Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, Ann. Appl. Prob., 1(1), 62–87.MATHCrossRefMathSciNetGoogle Scholar
  8. Gudynas, P. (1991). Refinements of the central limit theorem for homogeneous Markov chains, in Limit Theorems of Probability Theory, N.M. Ostianu (ed.), Akad. Nauk SSSR, Moscow, 200–218.Google Scholar
  9. Isaacson, D. (1976). Markov Chains:Theory and Applications, John Wiley, New York.MATHGoogle Scholar
  10. Jones, G. (2004). On the Markov chain central limit theorem, Prob. Surveys, 1, 299–320.Google Scholar
  11. Maxwell, M. and Woodroofe, M. (2000). Central limit theorems for additive functionals of Markov chains, Ann. Prob., 28(2), 713–724.MATHCrossRefMathSciNetGoogle Scholar
  12. Meyn, S.P. and Tweedie, R.L. (1993). Markov Chains and Stochastic Stability, Springer, New York.MATHGoogle Scholar
  13. Nagaev, S. (1957). Some limit theorems for stationary Markov chains, Teor. Veroyat-nost Primerien, 2, 389–416.MathSciNetGoogle Scholar
  14. Norris, J.R. (1997). Markov Chains, Cambridge University Press, Cambridge.MATHGoogle Scholar
  15. Roberts, G.O. and Rosenthal, J.S. (1997). Geometric ergodicity and hybrid Markov chains, Electron. Commun. Prob., 2, 13–25.MATHMathSciNetGoogle Scholar
  16. Rosenblatt, M. (1971). Markov Processes, Structure, and Asymptotic Behavior, Springer, New York.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anirban DasGupta
    • 1
  1. 1.Department of StatisticsPurdue UniversityWest Lafayette

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